Enumeration of standard Young tableaux of shifted strips with constant width

TL;DR

This paper derives recurrence relations for counting standard Young tableaux of truncated shifted shapes with fixed widths, revealing connections to Pell numbers and expanding combinatorial enumeration techniques.

Contribution

It introduces new recurrence relations for specific truncated shifted shapes and links one case to Pell numbers, advancing combinatorial enumeration methods.

Findings

Recurrence relations for g_{3,n}, g_{n,4}, g_{n,5} derived

g_{n,4} equals the (2n-1)-st Pell number

Provides integral method approach for enumeration

Abstract

Let $g_{n_1,n_2}$ be the number of standard Young tableau of truncated shifted shape with $n_1$ rows and $n_2$ boxes in each row. By using of the integral method this paper derives the recurrence relations of $g_{3,n}$, $g_{n,4}$ and $g_{n,5}$ respectively. Specially, $g_{n,4}$ is the $(2n-1)$-st Pell number.